Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/15106
Title: Maximum distance separable 2D convolutional codes
Author: Climent, J.-J.
Napp, D.
Perea, C.
Pinto, Raquel
Keywords: 2D convolutional code
Circulant Cauchy matrix
Generalized Singleton bound
Maximum distance separable code
Superregular matrix
Issue Date: Feb-2016
Publisher: IEEE
Abstract: Maximum distance separable (MDS) block codes and MDS 1D convolutional codes are the most robust codes for error correction within the class of block codes of a fixed rate and 1D convolutional codes of a certain rate and degree, respectively. In this paper, we generalize this concept to the class of 2D convolutional codes. For that, we introduce a natural bound on the distance of a 2D convolutional code of rate $k/n$ and degree $delta $ , which generalizes the Singleton bound for block codes and the generalized Singleton bound for 1D convolutional codes. Then, we prove the existence of 2D convolutional codes of rate $k/n$ and degree $delta $ that reach such bound when $n geq k (({(lfloor ({delta }/{k}) rfloor + 2)(lfloor ({delta }/{k}) rfloor + 3)})/{2})$ if $k {nmid } delta $ , or $n geq k (({(({delta }/{k}) + 1)(({delta }/{k}) + 2)})/{2})$ if $k mid delta $ , by presenting a concrete constructive procedure.
Peer review: yes
URI: http://hdl.handle.net/10773/15106
DOI: 10.1109/TIT.2015.2509075
ISSN: 0018-9448
Appears in Collections:CIDMA - Artigos
SCG - Artigos

Files in This Item:
File Description SizeFormat 
2DCCk_2014_v07_submitted.pdfPreprint447.36 kBAdobe PDFView/Open


FacebookTwitterDeliciousLinkedInDiggGoogle BookmarksMySpace
Formato BibTex MendeleyEndnote Degois 

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.